Price expectations and the supply of wastepaper

JOURNAL

OF ENVIRONMENTAL

Price

ECONOMICS

Expectations

AND

and Ro;v

Department

of Political

Economy,

University

MANAGEMENT

the Supply

6, 332-346

( 1979)

of Wastepaper

EDWARDS

of Aberdeen,

Old Aberdeen,

AB9

STY

Scotland

Received June 9, 1978; revised December 12, 1978 For some time the price response of the supply of wastepaper has been analyzed in terms of either static simultaneous equation models, or by the use of fairly ad hoc distributed lag models. This paper suggests that a model based on the price expectations of wastepaper suppliers is capable of explaining certain anomalies in earlier empirical work, and confirms the view that purely price-based policies to stimulate wastepaper recycling are likely to be ineffective. Not only is the supply of wastepaper insensitive to changes in price expectations, but the latter are themselves very slow to adjust to changes in actual prices.

INTRODUCTION It is clear that waste materials recycling has a role to play, albeit a limited one, in the conservation of resources and the reduction of environmental pollution. Various attempts have been made to assess the technical limitations to recycling and the feasibility of their removal. In the case of waste paper, such exercises are reported for the United States by the Midwest Research Institute [S] and Arthur D. Little, Inc. [S], and for the European Economic Community countries by Massus [lo]. The divergence between actual and feasible recycling levels is often substantial, indicating the necessity of significant price increases for recycling to take place at anywhere near full capacity. Mechanisms for achieving any increase have largely centered on the manipulation of prices, either through the removal of alleged discriminatory subsidies to virgin materials (see U.S. Environmental Protection Agency [lS]), or through some form of subsidy to recycling technologies (as is, for instance, the case with de-inking plants in the U.K.). Alternative suggestions include such mechanisms as buffer stock schemes to reduce fluctuations in secondary materials markets, These policy measures are discussed at greater length by Pearce [12]. One factor which is crucial to any such price-based policies is of course the elasticity of supply of waste materials, since this will determine the magnitude of any response by suppliers (voluntary agencies, merchants, municipalities) to price alterations and will consequently have greater implications for the feasibility, or likely success, of any intervention. To date, analyses of wastepaper supply can be roughly divided into two categories. The first includes those studies which relate supply to current price and other variables in market equilibrium models. Examples of this approach include work done by the R. T. I. [ll] which reveals an extremely low estimate 332 0095~of396/79/04032-09$02.00/0 Copyright All rights

0 1979 by Academic Press. Inc. of reproduction in any form reserved.

PRICES

AND

WASTEPAPER

SUPPLY

343

of the price elasticity of supply of around 0.09. The second main approach is the use of distributed lag functions, in which current levels of supply are related to various combinations of current and previous prices. Examples of this type of ana.lysis can be found in studies by Deadman et al. [3] for the United Kingdom, and Anderson and Spiegelman [2] and the Environmental Law Institute [4] for the United States. An interesting conclusion of these studies is that although supply is found to respond positively (albeit in an inelastic fashion) to current price, its relationship to previous price levels is negative>. This has the effect that the long-run (or total) price elasticity is even smaller than the short-run (01 immediate) figure. Without advancing any particular rationale, Dcadman et al. conclude that the negative coefficients on lagged prices arc “implausible.” The justification put forward in other studies (c.g., Anderson and Spicgelman) is that high prices in the previous period result in a drawing down of suppliers’ invcxntories, imposing a constraint on supply in the current period. This argument makes good sense in cases where lags of, say, only I month are considered, but it is not very satisfactory to use a similar rationale for negative weights on prices which are lagged by 3 months or a yrar. The reason for this is that suppliers’ inventories are very short-run phenomena (essentially functional transit inventory) and not very significant in magnitude, owing to high storagcx cost. Consequently, over a 3-month, or longer, period, there is more than sufficient, time for stock adjustments to take place, and for the tffcct of increased price levels to be absorbed by supplying agents. The only real const,raint over this sort of time span is the available collectable t,onnagc (which is in any case always btbing replenished), a constraint which has ncvcr been anywhere near binding. This, however, still leaves the observed negative weights on longer laggc>d price levels to be explained. An answer to this problem may bc found in a closes examination of the response of suppliers to the dynamics of what is, after all :I very volatile market. Whereas, up to now, most analyses have concentrated on what are essentially instantaneous equilibrium approaches in static frameworks, it may be more satisfactory to allow for an explicit,ly dynamic background to supply response. This analysis suggests one such dynamic interpretation of supply behavior, both as an alternative explanat,ion of existing campirical results and :LP:t basis for fresh econometric evidence. THE

MODEL

Although reflecting a continuous process, it is simpler and more easily amenable to econometric analysis to deal with the problem in terms of discrete time periods. The basic hypothesis is that the supplier (being a fairly optimistic price taker in both the United Kingdom and United States) will make his quantity decisions at the start of each period on the basis of the price he expects to prevail in that, period, as well as taking into account any other relevant circumstances, such as costs, and available waste. This leads to t’he specification : St = a + b.Pte + c.Xlr where S‘ PC

represents supply in period t, represents expected price in period t,

+ rl.Xzl +. . . + u,,

(1)

RON EDWARDS

334 X,1 Ut

represent other independent variables, represents a stochastic disturbance term, indicating not be completely deterministic.

that the decision need

The relationship is assumed to be linear in the absence of a priori evidence to the contrary. In its present form, this equation does not lend itself to statist.ical estimation since the expected price variable is unobservable. For the analysis to proceed it is necessary to form a subsidiary hypothesis on the determination of expectations. This can be achieved by the following reasoning: By definition, the expected price will be equal to the previous price plus the expected price change (2) where APL” = Pie - P,-1.

(3)

It seems reasonable to assume that this expected change in price will be based on the suppliers’ previous experience of price changes. In particular it is reasonable to assume that they will alter their expections about the change in prices on the basis of observed price changes in the following manner : APte = AP&

+ X(APt-1 - AP&),

O
(4)

i.e., the current expected rate of change in price is equal to the previous expected price change, plus some positive proportion, X, of the error that was made in the last period. If suppliers have underestimated the change in the previous period, they will revise their expectations for the current period upward, and vice versa. This is, of course, an application of the familiar adaptive expectations model to the case of changes in the unobservable variable rather than in the variable itself. The adoption of the hypothesis that suppliers update expectations about price changes instead of price levels is justified by a closer examination of the implicit assumptions of the mechanism (see, for example, Flemming [5, p. 621). The adaptive expectations model implies that suppliers have some idea of a “normal” value of the variable to which the mechanism is applied, since the coefficient X is restricted to lie between zero and unity (i.e., deviations from the “normal” value are not regarded as being totally permanent with the effect that the elasticity of expectations is restricted to be less than unity). In such a volatile market as that for wastepaper, it is highly unlikely that suppliers will have any conception of a normal price, around which deviations are regarded as temporary. It is much more probable that they well have (if anything) an idea about the “usual” rate of change of prices. It is consequently more satisfactory to use a model which allows for this, and to regard any expectations which are formed as being changes in price rather than about price levels. If this hypothesis is accepted as a reasonable basis for the determination of expectations, then Eq. (4) simply reduces to AP/

= (1 - h)APt-1” + XAP,+

which expresses the expected change in prices as a simple weighted previous expected, and actual, price changes.

(5) average of

PRICES

AND

WASTEPAPER

SUPPLY

33,s

By successively lagging Eq. (5), and resubstituting, it is possible to obtain a relationship between current expect,ed price a,nd an infinit’e number of previous actual price changes, i.c., APte = X 2 (1 - X)iAPt-~-i. This allows the original observable variables,

supply function

S, = a + bP,-1 + bX 5 (1 -

(1) to be written

X)“AP,-1-i

solely in terms of

+ cx,l +. . . + ?ct.

(7)

i=O

Note immediately that this supply function involves price changes, as well as as the more conventional price level. Even though the function is in terms of observable variables, it is still not possible to estimate its pa.rameters, since it, involves a geometrically declining lag on price changes of infinite length. However, by an appropriate Koyck transformation (see Johnston [7, p. 298-j) the function can be expressed as - a(1 - X)Pt-2 + Cxlt - (1 - X)CX&i +. . .+ (1 - X)St-1 + ut -

(1 - X)Ut-1

(8)

= Au + b(1 + A)P,-, - ZIP,-2 + CXll - (1 - X)CXM +*. . + (1 - X)S,&I + Ut -

(1 - X)&-1.

(9)

S, = Au + bxAP,-,

For simplicit,y, this may be rewritten

as

St = a + PPl-l + YPt-2 + OXll +

?Xl1-1

+.

.

+

/.lst-I

+

et.

(101

This equation is now in a suitable form for estimation, If the hypothesis put forward above is to be supported, then the estimated parameters should have the following properties : (i! (ii) (iii) (iv) (v) (vi) (vii)

B = y = -/3/r 6= ?j = 1+ j.4 =

b(l + A), P > 0, -b, y < 0, - 1 =x,0 0.

The important points to notice here are that (iv) and (v) imply that 6 and 1 should have opposite signs. If, as in the cases to be discussed later, collectable tonnage is entered as the independent variable, 6 should be positive, and q should be negative. Also, the values of x implicit in conditions (iii), (vi), and (vii) should be consistent with each other. If all of these conditions are met, it can obviously be inferred that the price change expectations hypothesis advanced does have empirical support. RESULTS

AND

ANALYSIS

Before analyzing the results obtained in estimating this model it is worthwhile to examine how consistent the hypothesis is with empirical evidence reported in

336

RON EDWARDS

other studies. First note that from Eq. (7) it is possible to derive an equation for supply in terms of an infinite series of lagged price levels, i.e., St = f(Pt-I,

Pt-2. . . .>.

(11) Now, since we expect X to be less than unity, a condition which must be met for the current hypothesis to be supported is that the coefficients on all but the most recent price level should be negative, and declining in magnitude, as can be seen in Eq. (7). The negative condition is indeed met in studies (which do examine past price levels) both by Anderson and Spiegelman [a], and by Deadman et aI. [a]. The magnitude condition is constrained to be true in Anderson and Spiegelman, since they use an Almon lag scheme whose weights decline over time. It is, however, impossible to determine whether the implied value of the adjustment parameter X is economically meaningful in the absence of more detailed information on the numerical scheme they adopted. The relative magnitudes of the estimated coefficients reported by Deadman et al. seem to be roughly in line with the requirements of the current mode. They estimate an equation of the form St = a + bP,-l - cP1+

(12)

which, using quarterly data for the United Kingdom for the period 1968 to 1976, yielded estimates of “b” and “c” of 0.75 and 0.72, respectively. Both coefficients were significantly different from zero, having t ratios of over 4 in both cases. The relative magnitudes of the coefficients imply a value of X of 0.0417, which is between zero and unity, as required. This sort of argument is, of course, very tentative, and the reexamination of empirical results previously obtained can never be anything but indirect. However, there are grounds at least for believing that there is some degree of consistency between existing econometric work and the current hypothesis. To gain more direct support, however, it is necessary to examine the results obta.ined in estimating the parameters of the current model, contained in Eq. (10). The data used in this analysis are derived from a monthly time series for the United States for the period 1960 to 1974, taken from the U.S. Department of Commerce L-15) and the U.S. Bureau of Labor Statistics [14], averaged and summed to produce quarterly observations on the price variables and flows, respectively. Quarterly data were preferred to monthly data, to overcome any potential short-lived stock adjustment problems (such as those suggested by Anderson and Spiegelman). A major difficulty in this context is the large amount of intraannual variation in consumption and purchases of wastepaper caused by holiday and peak-use periods. This is not reflected in price movements owing to institutional factors, and wa.s taken into account through appropriate dummy variables. The “other” independent variable in this case is the available collectable tonnage. The implied error structure of Eq. (10) does pose serious problems for estimation. Unless very specific circumstances prevail, the error term el will be serially correlated according to a moving average process, owing to the Koyck transformation. This, combined with the lagged endogenous variable on the right-hand side of the equation will result in biased and inconsistent OLS estimates. The equation was consequently estimated by the Zellner-Giesel search procedure [17], which involves “choosing” values for X, transforming the data, and estimating by

PRICES AND WASTEPAPER SUPPLY

337

TABLE I Unrestricted Estimates of Parameters in Eq. (10) using Quarterly Data PI -0.8

A” 0.1 -

OL -416.80 (13.18)*

P

c

Y

2.71 (3.38)

-2.28 (2.61)

(1Note that there is no estimate of p in Eq. b Figures in parenthesesare t statistics.

(10)

0.067 (2.05)

t -0.064 (1.95)

II= 0.988 -

DWI 1.58 --

sinceit is “chosen” to determine the value of X.

OLS. A more general procedure, which allows for the fact that the original error term in Eq. (1) may be serially correlated was used, in which values for the autocorrelation coefficient, p, are also selected, a.nd the appropriate data transformation is carried out before lea.&squares estimation. The objective is to find the pair of values of x and p for which the sum of squared residuals is a minimum. The resulting estimates should then leave all of the optimal properties of the OLS estimator under the classical consumptions. Note particularly that since the equation is in terms only of Zagged prices, there should be no danger of simultaneous equation bias in using this technique. The parameter estimates which resulted in the minimum sum of squared residual are given in Table I. (Since the dummy coefficients are largely irrelevant they are omitted owing to space considerations, though all were significantly different from zero). Since the data are quarterly, correlation was made for fourth-order serial correlation, and t,hr Durbin-Watson test applied for this. It is clear that conditions (i), (ii), (vi), and (v) are met by the signs of the estimated coefficients. The collectable tonnage variable and its lagged value do not, however, have coefficients significantly different from zero at the 5y0 level, indicating perhaps that the constraint of available waste is not important, over a !&month period. The values of h implied by conditions (iii) and (vi) arc 0.20 and 0.06, rrspcctivcly, lying within the permissible range of zero to unity, but displaying numerical difference from the “selected” value of 0.10. Unfortunately, there is no direct test of the statistical significance of these differences, since there is no estimate of the standard error of X. Also, since the implied values of X are derived from nonlinear transformations, we have no analytical idea of their distributional properties. There is, however, an indirect test which may be appropriate to this case. The fact that a particular value of x is “chosen” before the estimation implies two linear restrictions on the values of the parameters of the equation, i.e., P = --Cl + x)-Y,

(13)

Tj = -(l

(14)

and - X)6.

If the estimation procedure is repeated after imposing these restrictions, it. is possible to test whether or not there is any significant difference between the two regressions. If there is none, we cannot reject the hypothesis that the restrictions are valid. Although this is a long way from actually accepting the null hypothesis that the restrictions hold, and the logic of hypothesis testing is violated to some

RON EDWARDS

338

extent, this procedure can be read very cautiously as at least some indication of consistency. This test (see, for example, Maddala [9, p. 1971) involves calculating the F statistic (RSS - USS)/r F(,t-,c--ljr =

USS/(n

-

k -

(15)

1) ’

where

RSS USS r n k

is is is is is

the the the the the

restricted sum of squared residuals, unrestricted sum of squared residuals, number of restrictions, number of observations, number of parameters in the unrestricted

regression.

The imposition of restrictions (13) and (14) resulted in the parameter estimates given in Table II. This time there are no independent estimates of y and 7 since they are constrained by restrictions (13) and (14) and the selected value of X. The same X, p configuration resulted in the minimum sum of squares, and all parameters have the correct sign. An application of the F test described above yielded F&

= 2.5.

The difference between the regressions is insignificant at the 5% level, but becomes just significant at the 10% level, where the calculated figure is equal to the critical value. There are consequently some grounds for believing that the restrictions are not valid. However, given the interpretational problems of the test, and the percentage level at which it shows significant difference, these grounds are not strong. It appears that roughly 10% of any error made in the previous period is incorporated into expectations for the current period, reflecting a very slow adjustment process, though it is obviously very dangerous to speculate about precise numerical values in this sort of analysis. Nevertheless, the data do lend some support to the hypothesis in question, in that the totally unconstrained regression results in implied values of x which at least fall within the correct range, and goodness of fit and test statistics which are satisfactory. CONCLUSIONS

AND

POLICY

IMPLICATIONS

Although based on a different set. of behavioral assumptions, the practical implications of this analysis differ very little from those reached in earlier studies (see also Anderson [l] for similar conclusions with respect to lead). If anything, TABLE Restricted

-0.8 a Figures

0.1 in parentheses

Estimates

of Parameters

-412.92 (13.79Y are t statistics.

II in Eq.

0.79 (2.67)

(10) using

0.77 (4.86)

Quarterly

Data

0.987 -

1.60 -

PRICES

AND

WASTEPAPER TABLE

Unrestricted P

x

0.1 -

0.65 -

339

SUPPLY

III

Estimates of Parameters in Eq. (IO) using Annual Data 01

237.53 (0.23)”

P

7

6

67.35 (4.61)

-34.25 (2.56)

0.19 (5.36)

Rz

DW

0.945 -

1.76 -

t

-0.12 (3.00)

a Figures in parentheses are t statistics.

the implications for a price-orientated policy for the promotion of recycling are more pessimistic than before. According to the work carried out here, there arc two basic reasons for this. First, the elasticity of supply with respect to expected prices is very low. By returning from the estimated parameters to the original structural parameters in Eq. (l), the estimate of the elasticity at mean values is about 0.3. Consequently, very large changes in expected price would have to be achieved before the supply of waste paper would increase significantly. Second, changes in actual price (the policy instrument) do not feed instantaneously or totally through into expected prices. The adjustment process is very slow and imperfect. The interpretation is that suppliers, acting in the very volatile waste paper market would not immediately accept any price increase as being “permanent” enough to totally commit themselves, so that response to actual changes is both extremely sluggish and weak. These circumstances do not, of course, completely negate a price-based policy. If prices could be artificially increased by a large amount and held up over a period of time, the desired response could be achieved (though this is merely stating the obvious). They do, however, throw a great deal of doubt on the shortrun viability of such a policy, and indeed on the desirability of this type of action. APPENDIX Though there are grounds for believing that annual data are not really suitable for analyses involving adaptive expectations models (owing to the probability of full adjustment within the data period), given that the adjustment process appeared to be very slow in quarterly data it was felt that a repeat of the analysis using annual data might be interesting. This data, again for the United States but covering the period 1947 to 1973, is taken from Miedema et al. [ll]. The same estimation technique was used, but this time correction for first-order serial correlation is appropriate. Table III gives the results of the unconstrained regression. The results of a regression in which restrictions (13) and (14) were imposed a.re given in Table IV. TABLE Restricted

Estimates of Parameters

IV in Eq. (10) using Annual Data

P

x

a

P

6

R2

DW

0.1 -

0.65 -

1580.73 (4.27),=

49.49 (4.73)

0.22 (15.12)

0.941 -

1.66 -

o Figures in parentheses are t statistics.

340 Calculating

RON EDWARDS

the F statistic described in the text, it was found that Fd

This does not even become significant The coefficients suggest that about the previous period is incorporated further feature is that the coefficients highly significant, indicating perhaps over a period as long as a year.

= 1.75. at the 10% level. 6.575 of the error in expectations into expectations for the current on the collectable tonnage variable tha.t this constraint does become

made in year. A are now binding

REFERENCES 1. R. Anderson, Economic incentives for the recovery of secondary lead, Resource Recovery Consem. 2, (1977). 2. R. Anderson and R. Spiegelman, Tax policy and secondary material use, J. Environ. Econ. Manag. 4, 68-82 (1977). 3. D. Deadman, R. P. Grace, and R. K. Turner, Modelling the U.K. waste paper market, University of Leicester, mime0 (1977). 4. T. R. Durham and R. Anderson, “ Demand for Recyclable Materials,” Environmental Law Institute (1976). 5. J. Flemming, “Inflation,” Oxford Univ. Press, London/New York (1976). 6. W. E. Franklin, “Paper Recyling : The Art of the Possible, 1976-85,” Midwest Research Institute, New York (1973). 7. J. Johnston, “Econometric Methods,” 2nd ed., McGraw-Hill, New York (1972). 8. A. D. Little, Inc., “Analysis of the Demand and Supply for Secondary Fiber in the U.S. Paper and Paperboard Industry,” Environmental Protection Agency, Washington, D.C. (1976). 9. G. Maddala, “Econometrics,” McGraw-Hill, New York (1977). 10. M. Massus, “Waste Paper in the E.E.C.,” European Commission, Brussels (1974). 11. A. K. Miedema, Bun Song Lee, J. T. Rogoff, and P. C. Cooley, “The Case for Virgin Material Charges: A Theoretical and Empirical Evaluation in the Paper Industry,” Research Triangle Institute, Research Triangle Park, N.C. (1976). 12. D. W. Pearce, “The Economics of Waste Paper Recycling,” OECD, Paris (1977). Protection Agency, Washington, 13. F. Smith, Jr., “Waste Paper Supply Curve,” Environmental D.C. (1976). 14. U.S. Bureau of Labor Statistics, “Wholesale Prices and Price Indices,” Washington, D.C. 15. U.S. Department of Commerce, “Current Industrial Reports,” ser. M 26A, Washington, D.C. 16. U.S. Environmental Protection Agency, “Resource Recovery and Waste Reduction: Third Report to Congress,” Washington, D.C. (1975). 17. A. Zellner and M. S. Giesel, “Analysis of Distributed Lag Models with Applications to ConPaper presented to the European Meeting of the Ecosumption Function Estimation,” nometric Society (1968).